A Square Matrix A Over the Complexfield C Is Said to Be Idempotent If A2=A; Said to Bean Orthogonal Projector If It Is Both Idempotent and Hermitian, I.E., A2=A=A*,Where A* Denotes the Conjugate Transpose Of A. Fromthe Similarity Theory of Matrices, any Idempotent Matrix A Canbe Decomposed As , Where Ik Isthe Identity Matrix of Order K And K Is the Rank Of A;Any Orthogonal Projector A Can Be Decomposed As ,Where U-1=U*. Idempotent Matrices and Orthogonalprojectors Appear Almost Everywhere, and Have Been the Objects of Many Studiesin Matrix Theory and Its Applications.